Question 17·SAT Desmos Regression Practice·Algebra

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R(t)=kt+120

A company charges a total rental cost $R(t)$ , in dollars, to rent an electric bike for $t$ hours, where $k$ is a constant and $t>0$ . The total cost to rent the bike for 3 hours is $195. What is the total cost, in dollars, to rent the bike for 10 hours? (Disregard the $ sign when gridding your answer.)

Your answer

A linear model for a rental cost has two parts: a fixed charge and a charge that repeats each hour. A known rental time and total let you find the hourly charge; then you can evaluate the model at a new time. In Desmos, use a regression to find the unknown constant. Don't scale the whole known total, because the fixed charge is paid only once.

Hints

Hint 1
The $120$ in the model is a fixed charge, so it stays $120$ whether the bike is rented for $3$ hours or $10$ hours. What equation do you get when the time is $3$ and the total is $195$ ?
Hint 2
The coefficient $k$ is the charge per hour, not the total cost. Find $k$ from the $3$ -hour rental, then use the original model to get the 10-hour total.

Step-by-step

Find the hourly charge, then evaluate
Step 1
Turn the known rental into an equation
The $3$ -hour rental costs $195$ , so put $3$ in for $t$ and $195$ in for $R(t)$ : $195=3k+120$ . The $120$ is charged once, not once per hour. Separate the fixed charge from the hourly charge before finding a new total.
Step 2
Find the charge per hour
Type $195\sim3k+120$ in Desmos. The tilde asks Desmos to find the unknown rather than graph the equation. Under PARAMETERS, it shows $k=25$ , so the hourly charge is $25.
Step 3
Find the 10-hour total
Type $R(t)=kt+120$ , then $R(10)$ . Desmos uses $k=25$ and shows $R(10)=370$ . That includes the hourly charges and the fixed charge, so the total cost for $10$ hours is $370. Grid in 370.

Question 17·SAT Desmos Regression Practice·Algebra

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